Answer:
Option C - [tex]f(x)=(0.5)(0.2)^x[/tex]
Step-by-step explanation:
Given : The table of an exponential function.
To find : Which exponential function is represented by the table?
Solution :
First we create an exponential from the given table by taking any two values.
The general form of an exponential [tex]f(x)=ab^x[/tex]
Now, putting values from the table,
x=-2 and f(x)=12.5
[tex]12.5=ab^{-2}[/tex] ....[1] '
x=-1 and f(x)=2.5
[tex]2.5=ab^{-1}[/tex] ....[2]
Now, dividing [1] and [2]
[tex]\frac{12.5}{2.5}=\frac{ab^{-2}}{ab^{-1}}[/tex]
[tex]5=b^{-1}[/tex]
[tex]b=\frac{1}{5}[/tex]
[tex]b=0.2[/tex]
Substitute in [2]
[tex]2.5=a(0.2)^{-1}[/tex]
[tex]a=2.5\times 0.2[/tex]
[tex]a=0.5[/tex]
So, The exponential function with a=0.5 and b=0.2 is
[tex]f(x)=(0.5)(0.2)^x[/tex]
Therefore, Option C is correct.
